A 3-0 deficit also features in a brilliant book by economic theorist, Ariel Rubinstein. Economic Fables is part autobiographical, part an introduction to economic theory, and part critique of economic theory. In the last two pages of the book, Rubinstein describes the imaginary games of football played on his green-tiled bedroom floor. The 12x9 tiled floor replicated the dimensions of a football field, bowling pins became goalposts, and pieces of Lego became the teams and the ball. Rubinstein doubled as both the commentator and a striker on the blue Israeli team. He then describes the finish. "During most of the game, the rival team was ahead and held a 3:0 lead in the final minutes. But then, an unknown forward (that is, I) would score four goals to win a great victory for the team in blue."
The above example, and the book in general, provokes thoughts about what we value (and how we value). The 4-3 victory is the preferred one. Why did he not imagine a 4-0 victory? Why did his team have to overcome such a large deficit? Similar non-sporting issues are examined elsewhere in the book.
Sports economists are more likely to encounter the name of Ariel Rubinstein in discussions of tournament structures. For example, a paper from 1980 by Rubinstein is cited in a 2017 paper in the Journal of Sports Economics. The recent paper by Dagaev and Sonin is titled "Winning by Losing: Incentive Incompatibility in Multiple Qualifiers". The paper is motivated by a situation that arose in the Russian Premier League in May 2012. Russia had two Champions League places and four Europa League places to be allocated based on the results of the domestic league and cup results. The authors focus on a game between Lokomotiv and Sparta. They show that for a particular combination of results Lokomotiv would have been better off losing. While the situation did not come to pass, the authors suggest greater consideration of the incentive compatibility of tournaments is required.
Much of the relevant research on competition structure is located in literature outside of economics, e.g. Operations Research, Mathematics, and Computer Science. However, there is an increasing number of papers being published in economics journals that draw from these areas (possibly as a follow up to the Fort(Maxcy)-Zimbalist exchange of 2003). Two relatively recent papers published in the Journal of Sports Economics are worth noting. Jeroen Schokkaert and Johan Swinnen compare the theoretical predictions from Operations Research with the outcomes from the UEFA Champions League changes in tournament structure. Jiri Lahvicka (2015) takes a similar approach to the addition of a post-season knockout tournament to a regular season round-robin tournament in Czech ice hockey.
What makes the merging of the literatures exciting is the slight tension between the perspectives. Broadly speaking, the Operations Research is about finding a competition structure that identifies the "best" competitor at the least cost. Uncertainty of outcome is usually not viewed in a positive light. By contrast, the traditional sports economics literature highlights the importance of uncertainty of outcome. It will be interesting to see how the literature evolves.
But neither perspective truly captures what Rubinstein describes at the end of Economic Fables. There was no uncertainty of outcome as the author's imagination was going to ensure that Israel emerged victorious. And, the competition hardly produced the "best" competitor as it was determined by an unknown forward. He may not have made a name for himself in sport but he is a fine economic theorist.